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VeccTMVN (version 1.3.1)

Multivariate Normal Probabilities using Vecchia Approximation

Description

Under a different representation of the multivariate normal (MVN) probability, we can use the Vecchia approximation to sample the integrand at a linear complexity with respect to n. Additionally, both the SOV algorithm from Genz (92) and the exponential-tilting method from Botev (2017) can be adapted to linear complexity. The reference for the method implemented in this package is Jian Cao and Matthias Katzfuss (2024) "Linear-Cost Vecchia Approximation of Multivariate Normal Probabilities" . Two major references for the development of our method are Alan Genz (1992) "Numerical Computation of Multivariate Normal Probabilities" and Z. I. Botev (2017) "The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting" .

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install.packages('VeccTMVN')

Monthly Downloads

293

Version

1.3.1

License

GPL (>= 2)

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Repository

https://github.com/JCatwood/VeccTMVN

Maintainer

Jian Cao

Last Published

August 19th, 2025

Functions in VeccTMVN (1.3.1)

Simulate truncated multivariate normal (TMVT) using the Vecchia approximation

Univariate ordering under Vecchia approximation

Simulate truncated multivariate normal (TMVN) using the Vecchia approximation

Find ordered nearest neighbors based on a correlation Matrix. Assuming the absolute value of the correlation is monotonically decreasing with distance. Returns an n X (m + 1) matrix similar to `GpGp::find_ordered_nn`.

get_sp_inv_chol

Get the inverse upper Cholesky factor under the Vecchia approximation

FIC_reorder_univar

Univariate ordering under FIC approximation, first m chosen by m iter of dense univariate reordering

Applying the multi-level Monte Carlo (MLMC) technique to the pmvn function The function uses NLevel1 = 1 for m = m2 and the same exponential tilting parameter as m = m1 to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation

loglk_censor_MVN

Compute censored multivariate normal (MVN) log-probabilities that have spatial covariance matrices using Vecchia approximation

Compute multivariate normal (MVN) probabilities that have spatial covariance matrices using Vecchia approximation

Compute multivariate Student-t (MVT) probabilities that have spatial covariance matrices using Vecchia approximation

Applying the multi-level Monte Carlo (MLMC) technique to the pmvt function The function uses NLevel1 = 1 for m = m2 and the same exponential tilting parameter as m = m1 to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation

Simulate partially censored multivariate normal (MVN) at censored locations using the Vecchia approximation

Univariate variable reordering, described in Genz and Bretz (2009) If failed due to PD singularity, the unfinished order will be returned and a warning will be issued